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AP Precalculus Flashcards: Rational Functions And Zeros

Study Rational Functions And Zeros in AP Precalculus with focused flashcards that help you recognize the idea, recall the key rule, and apply it in practice-style prompts.

QUESTION

Identify a removable discontinuity in f(x)=x2−1x−1f(x) = \frac{x^2 - 1}{x - 1}.

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ANSWER

Removable discontinuity at x=1x = 1. The factor (x−1)(x-1) cancels from numerator and denominator.

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AP Precalculus: Polynomial and Rational Functions

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This deck focuses on Rational Functions And Zeros, giving you a quick way to review the definitions, rules, and examples that matter most for AP Precalculus.

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Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

Practice questions

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A rational function is a quotient of polynomials, f(x)=p(x)q(x)f(x)=\frac{p(x)}{q(x)}. Zeros are the xx-values where f(x)=0f(x)=0, which happens when p(x)=0p(x)=0 and q(x)≠0q(x)\neq 0. Vertical asymptotes occur where q(x)=0q(x)=0 and the factor does not cancel. Consider f(x)=x2−1x−1.f(x)=\frac{x^2-1}{x-1}. Factoring gives x2−1=(x−1)(x+1)x^2-1=(x-1)(x+1), so (x−1)(x-1) cancels for x≠1x\neq 1, leaving f(x)=x+1f(x)=x+1 with a hole at x=1x=1. The remaining zero is where x+1=0x+1=0, so x=−1x=-1 is a zero. Using the function provided, what are the zeros of f(x)=x2−1x−1f(x)=\frac{x^2-1}{x-1}?
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